Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-06-15




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 314.5030 216.1083 207.1305 196.2105 196.2506
Training 324.2904 145.9141 145.9562 147.2576 146.1410



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 257.7009 151.8762 149.3770 140.3657 140.2352
Training 261.4572 100.9766 100.6866 102.2896 101.5348



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -230.4437 -872.8758 -871.7695 -874.5867 -876.0296



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -230.0655 -845.3891 -844.3364 -847.806 -848.7406

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4504 6.3451 82.3883 94.3203 107.3392 94.1694
Precision for idtract 30.7244 4.2509 23.1165 30.4724 39.8230 30.0119
Precision for idqtr 3704.6708 3774.0461 555.1018 2589.2781 13619.6753 1361.1160
Rho for idqtr 0.2605 0.3581 -0.4721 0.2856 0.8484 0.3946
Precision for idqtr1 14301.7423 17584.8007 273.1949 8209.2304 61744.3916 355.9311



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 93.8570 6.3355 81.9415 93.6701 106.8796 93.3354
Precision for idtract (iid component) 89.4048 21.4854 54.3613 86.9966 138.4588 82.4177
Precision for idtract (spatial component) 90.7954 29.0560 47.3014 86.2868 159.9576 78.0003
Precision for idqtr 3792.3509 3860.6820 565.4267 2651.7892 13911.5723 1390.6478
Rho for idqtr 0.2750 0.3516 -0.4534 0.3031 0.8473 0.4202
Precision for idqtr1 13979.3751 17546.1124 228.0557 7797.4773 61265.0925 256.7190



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.2887 6.4024 82.2756 94.0900 107.4713 93.7213
Precision for idtract (iid component) 89.5066 21.5316 54.3636 87.1025 138.6481 82.5337
Precision for idtract (spatial component) 90.6540 29.0302 47.2829 86.1082 159.8489 77.7720
Precision for idqtr 4053.0293 4262.3198 600.4691 2786.2625 15215.0115 1457.7343
Rho for idqtr 0.2649 0.3561 -0.4674 0.2916 0.8471 0.4054
Precision for idqtr1 13172.5729 16462.9715 236.7183 7441.6621 57256.8436 294.1796
Precision for idtractqtr 18655.2645 18326.2824 1376.5669 13294.1741 66919.5269 3834.7584

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)